Year: 2025
Type: preprint
Abstract: Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously for the two algebras); these include being hyperfinite, atomic, diffuse and of type $I$, $II$ or $III$. Moreover, in all cases the canonical central projections of $M$ and $M^{\mathbb{G}}$ cutting out the summand with the respective property coincide. The result generalizes its classical-$\mathbb{G}$ analogue due to Jones-Takesaki.
Source: arXiv (Cornell University)
Author: Chirvasitu, Alexandru
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979253432
Cites:
Cited by:
Related to: